How do I center an object in its parent?
Your problem is essentially this one. With your current Pivot Point settings, ('Median',) the center of your object is considered to be the mean location of its vertices, not the center of its bounding box.

Set Pivot to 'Bounding Box'
Edit Mode, all selected, ShiftS,Cursor to Selected
Object mode, ShiftAltX Origin to Cursor
.. and set the location to 0..

...for both objects.